Using the trial equation method, a Broer-Kau-Kupershmidt （BKK） mechanism physical model is obtained, and the exact and approximate solitary traveling wave solutions are found. As an example, it is pointed out that the solitary traveling wave approximate solutions have better accurate degree by using the homotopic mapping theory.
A class of disturbed evolution equation is considered using a simple and valid technique. We first introduce the periodic traveling-wave solution of a corresponding typical evolution equation. Then the approximate solution for an original disturbed evolution equation is obtained using the asymptotic method. We point out that the series of approximate solution is convergent and the accuracy of the asymptotic solution is studied using the fixed point theorem for the functional analysis.
